Least Common Multiple (LCM) of 142 and 83
The least common multiple (LCM) of 142 and 83 is 11786.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 142 and 83?
First, calculate the GCD of 142 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 83 = 1 remainder 59 |
| 2 | 83 ÷ 59 = 1 remainder 24 |
| 3 | 59 ÷ 24 = 2 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 34 | 3434 |
| 11 and 158 | 1738 |
| 178 and 121 | 21538 |
| 185 and 106 | 19610 |
| 136 and 25 | 3400 |